Multiple methods would work, I'm sure.
One way would be to use automation on the effect, if the effect is automatable (not all may be).
Another common method would be to create a new track and place your effect on it. Then, slice up your original vocal track wherever you want the effect to occur and move those bits of track that you want the effect to happen for, down to the new track that you put your effect in. Now the only thing that will be processed by the effect are those bits of audio you placed in the track.
If you're dealing with multiple tracks that all need the same effect on them and all at the same time, you may be able to place your effect on an aux track and automate it to turn on and off as needed, being sure to route your multiple tracks aux sends to that effect/aux channel.
Forgive me if I'm not using the correct terminology for your tracks and routing in PT - I haven't used the program more than a handful of times and my reference is a different DAW, but it should be at least similar, I hope.